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Uniform bounds for
bilinear symbols with linear $K$-quasiconformally embedded
singularity
Marco Fraccaroli, Olli Saari and Christoph Thiele |
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Vol. 18 (2025), No. 9, 2293–2323
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Abstract |
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We prove bounds in the strict local range for trilinear Fourier multiplier forms with a -dimensional singular subspace. Given a fixed parameter , we treat multipliers with nondegenerate singularity that are push-forwards by -quasiconformal matrices of suitable symbols. As particular applications, our result recovers the uniform bounds for the one-dimensional bilinear Hilbert transforms in the strict local range, and it implies the uniform bounds for two-dimensional bilinear Beurling transforms, which are new, in the same range. |
Keywords
phase space localization, time-frequency analysis,
modulation-invariant operators, uniform estimates
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Mathematical Subject Classification
Primary: 42B15, 42C15
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Milestones
Received: 19 February 2024
Accepted: 29 October 2024
Published: 5 September 2025
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Authors |
| Marco Fraccaroli | |
| Basque Center for Applied
Mathematics Bilbao Spain |
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| Olli Saari | |
| Centre de Recerca Matemàtica Bellaterra Spain |
Departament de Matemàtiques Universitat Politècnica de Catalunya Barcelona Spain |
| Christoph Thiele | |
| Mathematisches Institut Universität Bonn Bonn Germany |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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